Do you mean being able to be pursue a specific type of engineering position/major or just having some kind of job title with the word “engineer”? The requirements are different for an electrical engineering technician, industrial engineer, and custodial engineer (I’ve really seen people using this term). Among my field within electrical engineering, there are some positions that regularly use math or physics beyond a high school level, but the vast majority do not. For example, some engineers have positions focusing on software coding, lab verification, sales, … that rarely use math or physics beyond a HS level. Or maybe you instead mean graduating with a bachelor’s degree at a 4-year college in an engineering major, while achieving a respectable 3.0+ GPA? I’d give different answers depending on the specific details.
That said, I’d expect the overwhelming majority of persons who meet your description (diligent, persistent, patient, have a good work ethic, reasonably intelligent, …) are capable of being an engineer. Some will have to work much harder than others, some will enjoy/dislike the work more than others, and some will struggle with various life difficulties unrelated to school or STEM; but one does not need to be a genius or have especially rare talents to be a general engineer.